Existence and upper semi-continuity of pullback attractors of a p-Laplacian equation with delay

Abstract

In this paper, we study the dynamics of a non-autonomous p-Laplacian equation with delay. We first prove the existence and uniqueness of solutions for this equation by using the Galerkin approximations. Then, applying the Sobolev compactness theorem, Ascoli-Azerla theorem, and energy method, we show the existence of pullback attractors for the associated process in space C([−h, 0]; Lp) as well as in space C([−h, 0]; L2). The upper semi-continuity result of the pullback attractors is also established here.